Solving Rational Inequalities

This video tutorial demonstrates how to solve and graph a rational inequality step-by-step. It begins with ensuring the inequality is set to zero, then factors the quadratic expression. Critical values are found by setting the numerator and denominator to zero. These values are tested on a number line to determine valid regions. The video concludes with the solution presented in various notations and a graph.

What is the first step in solving a rational inequality?

• Finding the critical points

• Factoring the denominator

• Ensuring zero is on one side

• Graphing the inequality

Why is it important to have zero on one side of the inequality?

• To ensure the inequality is in standard form

• To make factoring easier

• To simplify the graphing process

• To identify critical values

How do you find the critical values of a rational inequality?

• By setting the numerator and denominator to zero

• By solving for x in the inequality

• By graphing the inequality

• By factoring the entire inequality

What does a solid dot on the number line represent?

• A point where the inequality is undefined

• A region that is false

• A critical value that makes the inequality true

• A point that is not included in the solution

What is the purpose of dividing the number line into regions?

• To find the critical values

• To simplify the inequality

• To test each region for validity

• To graph the inequality

How is the solution of a rational inequality expressed?

• In graph form

• As a single number

• In interval notation

• As a polynomial